cel

The root cel- here comes from Latin celer, meaning 'swift, quick.' Its noun form was celeritas, 'speed' — the distant ancestor of celerity. This is a tight little root: most of its English family clusters around one idea, going faster.

The core engine is the prefixed verb. Take ad- ('to, toward') + celer and you get accelerate — literally 'to add swiftness to,' to make something go faster. The double 'c' comes from ad- assimilating before the c (ad- + cel → ac-cel). From that verb the whole sub-family unfolds mechanically: acceleration (the noun, the rate of speeding up — in physics, the rate of change of velocity), accelerated (the adjective, faster than normal: an accelerated course), and accelerating (the participle). The accelerator pedal in a car is named for exactly this.

Standing apart is celerity — the bare noun of speed, kept formal and literary. You won't hear it in conversation, but you'll meet it in older prose: 'he acted with great celerity.' It is the most direct survivor of celer itself.

Now the important warning, because this is where learners (and even dictionaries) get tangled. The words excel and excellent LOOK like they belong here — they contain 'cel' — but they do NOT come from celer ('swift'). They come from a completely separate Latin verb, excellere, built from ex- ('out, up') + -cellere ('to rise, to project'), related to celsus ('high, lofty'). Excellere meant 'to rise above, to surpass.' So to excel is to rise above others, and something excellent literally 'rises out' above the rest. There is no speed in it at all — the connection to celer is pure visual coincidence of spelling.

This is a textbook case of two unrelated roots wearing the same costume. If a word is about speed (accelerate, celerity), it's celer. If a word is about rising above / being superior (excel, excellent), it's the cellere root instead.